Acrylic acid and methacrylic acid polymers are polyacids known to be generally brittle in the molecular weight range used in this invention. Flexible compositions containing these polymers are desirable. The prior art teaches mixtures of certain phosphorus compounds with thermoplastic polymers. For example, U.S. Pat. No. 3,322,861 teaches use of diphosphonium halides in vinyl resins as flame retardants. However, it is not possible to predict which phosphorus compounds will flexibilize acrylic acid and methacrylic acid polymers. Therefore, it is unexpected and surprising to find that six phosphorus and/or halogen-containing components named hereinafter may be used to produce flexible polyacid compositions.